This paper studies voting over quadratic taxation when income is fixed and taxation non distortionary. The set of feasible taxes is compact and self-interested voters have corner preferences. We first show that, if a majority winning tax policy exists, it involves maximum progressivity. We then give a necessary and suficient condition on the income distribution for a majority winner to exist. This condition appears to be satisfied for a large class of distribution functions.
De Donder, P., & Hindriks, J. (2003). Majority support for progressive income taxation with corner preferences (ECON Discussion Papers 2003/02). https://hdl.handle.net/2078.5/36479